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numbers and algebraic expressions
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function and its properties
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polynomials
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exponential function
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trigonometry
plane geometry
analytic geometry
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combinatorics
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elements of statistics
kropki game
Trigonometric functions of sum and difference of two angles. sin(α+β) = sinαcosβ + cosαsinβ, cos(α+β) = cosαcosβ - sinαsinβ, tan(α+β) = tanα+tanβ / 1-tanαtanβ, cot(α+β) = cotαcotβ-1 / cotα+cotβ, sin(α-β) = sinαcosβ - cosαsinβ, cos(α-β) = cosαcosβ + sinαsinβ, tan(α-β) = tanα-tanβ / 1+tanαtanβ, cot(α-β) = cotαcotβ + 1 / cotβ - cotα. Trigonometric functions of double and triple angle. sin2α = 2sinαcosα, cos2α = cos^2α-sin^2α, tan2α = 2tanα / 1-tan^2α, cot2α = cot^2α-1 /2cotα, sin3α = 3sinα-4sin^3α, cos3α = 4cos^3α-3cosα, tan3α = 3tanα-tan^3α / 1-3tan^2α, cot3α = cot^3α - 3cotαo3cot^2α-1. Derivations.